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Glossary |
Catalog of Isomorphism Classes of Oriented Matroids
The following table shows the number of isomorphism classes of oriented matroids
(where card is the cardinality of a simple representative).
Data can be accessed by clicking on the corresponding number (if available):
|
|
| |
card = 2 |
card = 3 |
card = 4 |
card = 5 |
card = 6 |
card = 7 |
card = 8 |
card = 9 |
card = 10 |
| rank = 2 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
| rank = 3 (dim = 2) |
1 |
2 |
4 |
17 |
143 |
4 890 |
461 053 |
95 052 532 |
| rank = 4 (dim = 3) |
1 |
3 |
12 |
206 |
181 472 |
unknown |
unknown |
| rank = 5 (dim = 4) |
1 |
4 |
25 |
6 029 |
unknown |
unknown |
| rank = 6 (dim = 5) |
1 |
5 |
50 |
508 321 |
unknown |
| rank = 7 (dim = 6) |
1 |
6 |
91 |
unknown |
| rank = 8 (dim = 7) |
1 |
7 |
164 |
| rank = 9 (dim = 8) |
1 |
8 |
| rank = 10 (dim = 9) |
1 |
|
Cardinality = 10, rank = 9 (dimension = 8)
List of the 8 representatives of IC(10,9), ordered by the RevLex-Index.
The numbers above the signs indicate the elements of the corresponding basis.
1111111112
2222222233
3333333444
4444445555
5555566666
6666777777
7778888888
8899999999
9aaaaaaaaa
IC(10,9,1) = ++++++++++
IC(10,9,2) = 0+++++++++
IC(10,9,3) = 00++++++++
IC(10,9,4) = 000+++++++
IC(10,9,5) = 0000++++++
IC(10,9,6) = 00000+++++
IC(10,9,7) = 000000++++
IC(10,9,8) = 0000000+++